Many math teachers now ask students to explain their thinking in writing, whether in a short constructed response, a journal entry, or a problem-solving write-up. The practice reveals what a correct answer can hide, such as lucky guessing, a memorized procedure with no understanding, or a clever method the student could not otherwise show. It also exposes the opposite, a student with strong understanding who loses points because the written steps are incomplete.

Grading these responses is difficult for teachers who are not trained as writing teachers. They worry about penalizing students for weak language, are unsure how much explanation is enough, and find that reading paragraphs takes far longer than checking answers. A clear scoring guide can address each concern, and students benefit even more from knowing exactly what the teacher is looking for before they begin writing.

The approach below focuses on mathematical reasoning and treats writing as the vehicle. It works for middle school through introductory college courses. A teacher does not need a background in writing instruction to use it, only a willingness to read explanations as evidence of thinking. Even a few minutes of attention to the words students choose will show where understanding is solid and where it is borrowed from a memorized procedure.

Define what a complete explanation contains

Tell students what a full explanation includes: the strategy they chose and why, the key steps with the reasoning behind each, and a check of whether the answer makes sense. Show an example at three levels, such as a response that states only the answer, one that lists steps without reasons, and one that connects each step to a mathematical idea. Students who see the difference are more likely to write the strongest version.

• Show sample explanations at three levels of completeness
• Score correctness, reasoning, and clarity as separate criteria
• Accept diagrams, equations, and sentence frames as explanation
• Name the specific idea that is missing in each comment
• Assign short explanation tasks a few times a week

Score reasoning separately from language

Use a short rubric with three criteria: correctness of the math, quality of reasoning, and clarity of communication. Weight the first two most heavily, and tell students that clarity means the reader can follow the logic, not that the grammar must be perfect. This protects multilingual learners and students who struggle with writing, and it keeps the focus on the math.

Allow diagrams, equations, and sentence frames as valid ways to explain. A well-labeled picture can show reasoning that is hard to put into words. Sentence starters such as I know this because and I checked by can help students who do not know where to begin, and they can be faded gradually over the semester as students gain confidence in explaining their thinking on their own.

Give feedback that targets the thinking

Comments should name the specific idea that is missing or misunderstood, not just mark the answer wrong. A note such as you divided both sides but did not explain why that keeps the equation balanced points to the concept. Ask a question the student can answer in the next attempt, such as what would happen if the value were negative.

Look for common patterns across the class and address them in a mini-lesson. If many students describe a procedure without explaining why it works, the whole class benefits from a conversation about the reasons. A few strong sample explanations, shared anonymously, serve as models, and showing a range of strategies helps students see that more than one method can be correct and well explained.

Make it manageable and keep it regular

Use short prompts, and assign explanation tasks a few times a week instead of on every problem. Score some responses fully and give others a quick check mark with a single comment. A mix of depth and speed keeps the workload reasonable, and it lets the teacher spend the most careful reading on the responses that reveal the most about student thinking, such as those about a new idea or a persistent misconception.

Where a rubric-based tool is permitted, it can help sort responses by whether they include reasoning and flag ones that merely state steps, with the teacher reviewing mathematical accuracy. Teachers remain the judges of whether the mathematics is sound. Over a semester, students who write regularly about their reasoning often show improved understanding on tests as well, which suggests the habit is worth the time it takes.